1. Wang, Y. E., Wei, G.-Y. & Brooks, D. Benchmarking TPU, GPU, and CPU platforms for deep learning. Preprint at arXiv https://doi.org/10.48550/arXiv.1907.10701 (2019).

2. Wright, L. G. et al. Deep physical neural networks trained with backpropagation. Nature 601, 549–555 (2022).

   Article 

   Google Scholar 

3. Wetzstein, G. et al. Inference in artificial intelligence with deep optics and photonics. Nature 588, 39–47 (2020).

   Article 

   Google Scholar 

4. Shastri, B. J. et al. Photonics for artificial intelligence and neuromorphic computing. Nat. Photonics 15, 102–114 (2021).

   Article 

   Google Scholar 

5. Yao, P. et al. Fully hardware-implemented memristor convolutional neural network. Nature 577, 641–646 (2020).

   Article 

   Google Scholar 

6. Okumura, S. et al. Nonlinear decision-making with enzymatic neural networks. Nature 610, 496–501 (2022).

   Article 

   Google Scholar 

7. Mehonic, A. & Kenyon, A. J. Brain-inspired computing needs a master plan. Nature 604, 255–260 (2022).

   Article 

   Google Scholar 

8. Farhat, N. H., Psaltis, D., Prata, A. & Paek, E. Optical implementation of the Hopfield model. Appl. Opt. 24, 1469–1475 (1985).

   Article 

   Google Scholar 

9. Weaver, C. & Goodman, J. W. A technique for optically convolving two functions. Appl. Opt. 5, 1248–1249 (1966).

   Article 

   Google Scholar 

10. Shen, Y. et al. Deep learning with coherent nanophotonic circuits. Nat. Photonics 11, 441–446 (2017).

    Article 

    Google Scholar 

11. Tait, A. N. et al. Neuromorphic photonic networks using silicon photonic weight banks. Sci. Rep. 7, 7430 (2017).

    Article 

    Google Scholar 

12. Feldmann, J. et al. Parallel convolutional processing using an integrated photonic tensor core. Nature 589, 52–58 (2021).

    Article 

    Google Scholar 

13. Xu, X. et al. 11 TOPS photonic convolutional accelerator for optical neural networks. Nature 589, 44–51 (2021).

    Article 

    Google Scholar 

14. Anderson, M. G., Ma, S.-Y., Wang, T., Wright, L. G. & McMahon, P. L. Optical transformers. Preprint at arXiv https://doi.org/10.48550/arXiv.2302.10360 (2023).

15. Lin, X. et al. All-optical machine learning using diffractive deep neural networks. Science 361, 1004–1008 (2018).

    Article 
    MathSciNet 

    Google Scholar 

16. Chang, J., Sitzmann, V., Dun, X., Heidrich, W. & Wetzstein, G. Hybrid optical-electronic convolutional neural networks with optimized diffractive optics for image classification. Sci. Rep. 8, 12324 (2018).

    Article 

    Google Scholar 

17. Miscuglio, M. et al. Massively parallel amplitude-only fourier neural network. Optica 7, 1812–1819 (2020).

    Article 

    Google Scholar 

18. Gigan, S. Imaging and computing with disorder. Nat. Phys. 18, 980–985 (2022).

    Article 

    Google Scholar 

19. Saade, A. et al. in 2016 IEEE International Conference on Acoustics, Speech and Signal Processing 6215–6219 (IEEE, 2016). https://doi.org/10.1109/ICASSP.2016.7472872

20. Larger, L. et al. Photonic information processing beyond turing: an optoelectronic implementation of reservoir computing. Opt. Express 20, 3241–3249 (2012).

    Article 

    Google Scholar 

21. Brunner, D., Soriano, M. C., Mirasso, C. R. & Fischer, I. Parallel photonic information processing at gigabyte per second data rates using transient states. Nat. Commun. 4, 1364 (2013).

    Article 

    Google Scholar 

22. Vandoorne, K. et al. Experimental demonstration of reservoir computing on a silicon photonics chip. Nat. Commun. 5, 3541 (2014).

    Article 

    Google Scholar 

23. Larger, L. et al. High-speed photonic reservoir computing using a time-delay-based architecture: million words per second classification. Phys. Rev. X 7, 011015 (2017).

    Google Scholar 

24. Rafayelyan, M., Dong, J., Tan, Y., Krzakala, F. & Gigan, S. Large-scale optical reservoir computing for spatiotemporal chaotic systems prediction. Phys. Rev. X 10, 041037 (2020).

    Google Scholar 

25. Pierangeli, D., Marcucci, G. & Conti, C. Photonic extreme learning machine by free-space optical propagation. Photonics Res. 9, 1446–1454 (2021).

    Article 

    Google Scholar 

26. Van der Sande, G., Brunner, D. & Soriano, M. C. Advances in photonic reservoir computing. Nanophotonics 6, 561–576 (2017).

    Article 

    Google Scholar 

27. Spall, J., Guo, X. & Lvovsky, A. I. Hybrid training of optical neural networks. Optica 9, 803–811 (2022).

    Article 

    Google Scholar 

28. Zuo, Y. et al. All-optical neural network with nonlinear activation functions. Optica 6, 1132–1137 (2019).

    Article 

    Google Scholar 

29. Ryou, A. et al. Free-space optical neural network based on thermal atomic nonlinearity. Photonics Res. 9, B128–B134 (2021).

    Article 

    Google Scholar 

30. Feldmann, J., Youngblood, N., Wright, C. D., Bhaskaran, H. & Pernice, W. H. All-optical spiking neurosynaptic networks with self-learning capabilities. Nature 569, 208–214 (2019).

    Article 

    Google Scholar 

31. Tait, A. N. et al. Silicon photonic modulator neuron. Phys. Rev. Appl. 11, 064043 (2019).

    Article 

    Google Scholar 

32. Ashtiani, F., Geers, A. J. & Aflatouni, F. An on-chip photonic deep neural network for image classification. Nature 606, 501–506 (2022).

    Article 

    Google Scholar 

33. Wang, T. et al. Image sensing with multilayer nonlinear optical neural networks. Nat. Photonics 17, 408–415 (2023).

    Article 

    Google Scholar 

34. Williamson, I. A. D. et al. Reprogrammable electro-optic nonlinear activation functions for optical neural networks. IEEE J. Sel. Top. Quantum Electron. 26, 1–12 (2020).

    Article 

    Google Scholar 

35. Li, H.-Y. S., Qiao, Y. & Psaltis, D. Optical network for real-time face recognition. Appl. Opt. 32, 5026–5035 (1993).

    Article 

    Google Scholar 

36. Wagner, K. & Psaltis, D. Multilayer optical learning networks. Appl. Opt. 26, 5061–5076 (1987).

    Article 

    Google Scholar 

37. Marcucci, G., Pierangeli, D. & Conti, C. Theory of neuromorphic computing by waves: machine learning by rogue waves, dispersive shocks, and solitons. Phys. Rev. Lett. 125, 093901 (2020).

    Article 

    Google Scholar 

38. Nakajima, M., Tanaka, K. & Hashimoto, T. Neural Schrödinger equation: physical law as deep neural network. IEEE Trans. Neural Netw. Learn. Syst. 33, 2686–2700 (2021).

    Article 

    Google Scholar 

39. Zhou, T., Scalzo, F. & Jalali, B. Nonlinear Schrödinger kernel for hardware acceleration of machine learning. J. Light. Technol. 40, 1308–1319 (2022).

    Article 

    Google Scholar 

40. Teğin, U., Yıldırım, M., Oğuz, İ., Moser, C. & Psaltis, D. Scalable optical learning operator. Nature Comp. Sci. 1, 542–549 (2021).

    Article 

    Google Scholar 

41. Morandi, A., Savo, R., Müller, J. S., Reichen, S. & Grange, R. Multiple scattering and random quasi-phase-matching in disordered assemblies of LiNbO₃ nanocubes. ACS Photonics 9, 1882–1888 (2022).

    Article 

    Google Scholar 

42. Savo, R. et al. Broadband Mie driven random quasi-phase-matching. Nat. Photonics 14, 740–747 (2020).

    Article 

    Google Scholar 

43. Moon, J., Cho, Y.- C., Kang, S., Jang, M. & Choi, W. Measuring the scattering tensor of a disordered nonlinear medium. Nat. Phys. 19, 1709–1718 (2023).

44. Antonik, P., Marsal, N., Brunner, D. & Rontani, D. Human action recognition with a large-scale brain-inspired photonic computer. Nat. Mach. Intell. 1, 530–537 (2019).

    Article 

    Google Scholar 

45. Mounaix, M. et al. Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix. Phys. Rev. Lett. 116, 253901 (2016).

    Article 

    Google Scholar 

46. Popoff, S. M. et al. Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media. Phys. Rev. Lett. 104, 100601 (2010).

    Article 

    Google Scholar 

47. Mavi, A. A new dataset and proposed convolutional neural network architecture for classification of American Sign Language digits. Preprint at arXiv https://doi.org/10.48550/arXiv.2011.08927 (2020).

48. tecperson. Sign language MNIST. kaggle https://www.kaggle.com/datasets/datamunge/sign-language-mnist (2017).

49. LeCun, Y., Bottou, L., Bengio, Y. & Haffner, P. Gradient-based learning applied to document recognition. Proc. IEEE 86, 2278–2324 (1998).

    Article 

    Google Scholar 

50. Xiao, H., Rasul, K. & Vollgraf, R. Fashion-MNIST: a novel image dataset for benchmarking machine learning algorithms. Preprint at arXiv https://doi.org/10.48550/arXiv.1708.07747 (2017).

51. Oguz, I. et al. Programming nonlinear propagation for efficient optical learning machines. Adv. Photonics 6, 016002–016002 (2024).

    Article 

    Google Scholar 

52. Momeni, A. & Fleury, R. Electromagnetic wave-based extreme deep learning with nonlinear time-floquet entanglement. Nat. Commun. 13, 2651 (2022).

    Article 

    Google Scholar 

53. Krizhevsky, A. et al. Learning multiple layers of features from tiny images (2009).

54. Coates, A., Ng, A. & Lee, H. in Proc. Fourteenth International Conference on Artificial Intelligence and Statistics 215–223 (JMLR Workshop and Conference Proc., 2011).

55. Pierangeli, D., Rafayelyan, M., Conti, C. & Gigan, S. Scalable spin-glass optical simulator. Phys. Rev. Appl. 15, 034087 (2021).

    Article 

    Google Scholar 

56. Gerritsma, J., Onnink, R. & Versluis, A. Yacht hydrodynamics. UCI Mach. Learn. Reposit. https://doi.org/10.24432/C5XG7R(2013).

57. Yeh, I.- C. Concrete compressive strength. UCI Mach. Learn. Reposit. https://doi.org/10.24432/C5PK67 (2007).

58. Yan, X. & Han, J. in Proc. 2002 IEEE International Conference on Data Mining, 2002 721–724 (IEEE, 2002). https://doi.org/10.1109/ICDM.2002.1184038

59. Bronstein, M. M., Bruna, J., LeCun, Y., Szlam, A. & Vandergheynst, P. Geometric deep learning: going beyond euclidean data. IEEE Signal Process. Mag. 34, 18–42 (2017).

    Article 

    Google Scholar 

60. Yanardag, P. & Vishwanathan, S. in Proc. 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining 1365–1374 (2015). https://doi.org/10.1145/2783258.2783417

61. Shervashidze, N., Vishwanathan, S., Petri, T., Mehlhorn, K. & Borgwardt, K. in Artificial Intelligence and Statistics 488–495 (PMLR, 2009).

62. Yan, T. et al. All-optical graph representation learning using integrated diffractive photonic computing units. Sci. Adv. 8, eabn7630 (2022).

    Article 

    Google Scholar 

63. Ghanem, H., Keriven, N. & Tremblay, N. in ICASSP 2021–2021 IEEE International Conference on Acoustics, Speech and Signal Processing 3575–3579 (IEEE, 2021). https://doi.org/10.1109/ICASSP39728.2021.9413614

64. Lee, C. & Wilkinson, D. J. A review of stochastic block models and extensions for graph clustering. Appl. Netw. Sci. 4, 1–50 (2019).

    Article 

    Google Scholar 

65. Kersting, K., Kriege, N. M., Morris, C., Mutzel, P. & Neumann, M. Benchmark data sets for graph kernels. TU Dortmund http://graphkernels.cs.tu-dortmund.de (2016).

66. Müller, J. S., Morandi, A., Grange, R. & Savo, R. Modeling of random quasi-phase-matching in birefringent disordered media. Phys. Rev. Appl. 15, 064070 (2021).

    Article 

    Google Scholar 

67. Ni, F., Liu, H., Zheng, Y. & Chen, X. Nonlinear harmonic wave manipulation in nonlinear scattering medium via scattering-matrix method. Adv. Photonics 5, 046010–046010 (2023).

    Article 

    Google Scholar 

68. Hinton, G. The forward-forward algorithm: some preliminary investigations. Preprint at arXiv https://doi.org/10.48550/arXiv.2212.13345 (2022).

69. Krastanov, S. et al. Room-temperature photonic logical qubits via second-order nonlinearities. Nat. Commun. 12, 191 (2021).

    Article 

    Google Scholar 

70. Weis, R. S. & Gaylord, T. K. Lithium niobate: summary of physical properties and crystal structure. Appl. Phys. A 37, 191–203 (1985).

    Article 

    Google Scholar 

71. Wang, H. Nonlinear optical computing with disordered media. Zenodo https://doi.org/10.5281/zenodo.10799862 (2024).

72. Wang, H. Nonlinear optical computing with disordered media—experimental data for results in supplementary information. Zenodo https://doi.org/10.5281/zenodo.8392103 (2023).

Download references